We present a new approach to the eigensystem multiscale analysis (EMSA) for random Schrödinger operators that relies on the Wegner estimate. The EMSA treats all energies of the finite volume operator in an energy interval at the same time, simultaneously establishing localization of all eigenfunctions with eigenvalues in the energy interval with high probability. It implies all the usual manifestations of localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization). The new method removes the restrictive level spacing hypothesis used in the previous versions of the EMSA. The method is presented in the context of the Anderson model, allowing for single-site probability distributions that are Hölder continuous of order \(\alpha \in (0,1]\).

中文翻译：

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基于Wegner估计的Anderson模型本征系统多尺度分析

我们提出了一种基于Wegner估计的随机Schrödinger算子本征系统多尺度分析（EMSA）的新方法。EMSA同时处理一个能量间隔中的有限体积算子的所有能量，同时以高概率同时建立具有该能量值中的特征值的所有本征函数的局部化。它暗示了定位的所有通常表现（具有指数衰减的本征函数的纯点谱，动态定位）。新方法消除了以前版本的EMSA中使用的限制性层间距假说。该方法是在Anderson模型的上下文中提出的，允许单点概率分布为Hölder连续\（\ alpha \ in（0,1] \）阶数。